Campus

Gainesville

Publication date

1-23-2020

Publisher

Journal of Mathematical Physics 61, 013507 (2020)

Book or Journal Information

Journal of Mathematical Physics https://aip.scitation.org/doi/10.1063/1.5085004

Abstract

This paper is focused on the generalized Forchheimer flows for slightly compressible fluids, described as a system of two nonlinear degenerating partial differential equations of first order. We prove the existence and uniqueness of the Dirichlet problem for the stationary case. The technique of semidiscretization in time is used to prove the existence for the time-dependent case.

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EXISTENCE OF A SOLUTION FOR GENERALIZED FORCHHEIMER FLOW IN POROUS MEDIA WITH MINIMAL REGULARITY CONDITIONS

This paper is focused on the generalized Forchheimer flows for slightly compressible fluids, described as a system of two nonlinear degenerating partial differential equations of first order. We prove the existence and uniqueness of the Dirichlet problem for the stationary case. The technique of semidiscretization in time is used to prove the existence for the time-dependent case.